A 2-Skate, short for a Two-Inline-Ice-Skates-Single-Track-Vehicle, was built to show that without wheels, gyroscopic effects, fork angle, trail and power-to-the-wheels, a person could ride it. But the rider might have been a circus acrobat that can also sit backwards on his bicycle handlebar, and pedal while juggling and turning around in a circle. So this current study aimed at determining if normal persons can ride the 2-Skate with confidence, with the same phase lag between torso and vehicle leaning while slaloming, and the same torso and vehicle lean angles in steady state curves as predicted. A protocol was designed and 13 independent riders tested the 2-Skates. On their first trial, with the exception of a 79 year old, they could all ride it and go slaloming. Three did the phase lag and lean angle tests and obtained similar results, confirming the prediction of the Torso-Arms-Handlebar Steering Theory first presented by Ethier (1974), with differential non-holonomic and servomechanism system equations, and further explained on the web with access to recently revised equations. This confirmation (a) sheds light on how bicycles are steered, (b) clarifies that Countersteering is done automatically at low speeds, (c) supports and clarifies the way mountain bike steering is taught, (d) suggests a slight modification of the way motorcycle Countersteering is taught, (e) can be used to develop a different approach to 2-Wheeler simulators, (f) and can renew interest for motorcycles with seat belts and protective structure like the BMW-C1, and the closed-cabin electric motorcycles like the ultra-low drag and award winning Peraves e-Tracer.

This contribution presents an analysis of the vertical tyre stiffness of 20” bicycle tyres as usually mounted on bicycle carriers for the transport of children. The current research contributes to the science on bicycle comfort with the focus on the next generation cyclists. Two different methods to measure vertical or radial tyre stiffness of bicycle tyres are presented – a dynamic approach on a dynamic press and a static approach. Parameters modified are tyre inflation pressure and vertical load in the static experiment. In the dynamic experiment additionally dynamic load and frequency are varied. The dynamic experiments are performed on two different tyres. The same tyres are also used for the static experiments and completed with a third tyre, which is a clincher version of the narrow foldable tyre. The tyres are made for 406mm rim diameter as usually for bicycle carriers since the comfort of children in bicycle transportation is the larger scope behind the experiments. The main findings are as follows: • The stiffness of the tyres is in a range of 31 N / mm to 147 N / mm. It must be considered that values below 50 N /mm are related to extremely low inflation pressure that probably do not work reliably because the rim will puncture the tube. • Tyre inflation pressure is the main factor that controls the vertical stiffness. • Type of tyre (balloon vs. narrow tyre) hardly affects the stiffness. • The dynamic stiffness at 1 Hz is slightly higher than the static stiffness. • With increasing excitation frequency the stiffness increases, however, this effect is non-linear and varies between 3.7% at high pressure in the narrow tyre and up to 20% at low pressure in the balloon tyre. • Similarly, there is a trend to higher stiffness with increasing vertical load in a magnitude of 20% increase.

Microscopic simulation is an established tool in traffic engineering and research, where aggregated traffic performance measures are inferred from the simulation of individual agents. Additionally, measures describing the safety and efficiency of road user interactions gain importance for recent developments such as automated vehicles and urban cycling. However, current simulation frameworks model interactions including cyclists only with limited realism. To address this issue, we propose to bring bicycle dynamics to traffic simulation. We demonstrate that a novel reformulation of the social force framework can create input signals for a controlled inverted pendulum bicycle model and thereby enable a fully two-dimensional open space simulation of cyclist interactions. The inverted pendulum model introduces the need to stabilize the bicycle as a constraint to the reactive behavior of simulated cyclists. Furthermore, it enables the simulation of countersteering and weaving for stabilization. Our cyclist social forces have anisotropic force fields with respect to relative interaction position and orientation to describe the varying interaction constellations in open space. With these models, we simulate five single- and multi-cyclist test cases and show that the generated trajectories notably differ from results obtained from a 2D bicycle model without lean angle simulation. Measurements of the maximum lateral path deviation and post-encroachment time show that these differences are relevant for typical applications. Our work demonstrates the potential of introducing physics-based realistic bicycle dynamics to the microscopic simulation of individual road user interactions and the fundamental capability of our reformulated cyclist social forces to do so. Going further, we plan to calibrate and validate our model based on naturalistic cycling data to support the initial results of this work.

Since the concept of a Personal Mobility Vehicle (PMV) that tilts inward while turning is relatively new, there is currently a lack of theoretical considerations regarding the suspension mechanism. Therefore, this study aims to explore the theoretical relationship between suspension geometry and the pitching posture during turning in a PMV with two front wheels and one rear wheel that tilts inward during turns. Our findings suggest that a combination of a front telescopic suspension and a rear full trailing arm (swing arm) suspension is suitable for minimizing both the squatting pitching of the vehicle body during turns and the disturbances caused by changes in tread and tire camber angles during wheel strokes in the upright driving position from a static force balance perspective. From a dynamic perspective, there is no significant concern about pitching occurring even in cases where there may be a delay in active tilt angle tracking (PID) control when using the combination of front telescopic suspension and rear full trailing arm suspension. However, it is essential to note that a large sprung roll moment of inertia can still induce the squatting pitching.

Conference paper

The suspension system of a vehicle is essentially conceived with two objectives: to provide comfort to the passengers and maintain tires in contact with the ground (roadholding). It is well known, however, that optimal comfort and roadholding cannot be achieved simultaneously since they require a different set of stiffness and damping. Simple models are used to comprehend the variables involved with which the response acceleration, tyre force and suspension displacements due to random roads had been derived, together with optimal suspensions. Nonetheless the required suspension travel and suspension sag have not been extensively discussed. In this article we derive expressions to determine the suspension travel and suspension sag (static compression) required to transit a random road. It was also analysed the case when the optimal suspensions are used, and the expressions where simplified. Lastly, a numerical example show that the derived equations provide reasonable values for a first approximation.

Motorcycles are systems with complex dynamic behaviour that can become unstable under certain driving conditions. Avoiding such instabilities from the design stage is not trivial since they depend on various interrelated parameters, one of which is aerodynamics. Aerodynamic forces in a vehicle can be essentially described by its longitudinal (drag) and vertical (lift) components acting in a point known as the centre of pressure (CoP). Additionally, several authors explain that drag influences stability through four mechanisms: dampening lateral motion and changing weight distribution, tire cornering stiffness, and rake geometry. On the other hand, the lift force, which has been used importantly in sports motorcycles in recent years, can also influence stability, however, its effect has not been described in the literature. Therefore the aim of this research is to analyse the influence of lift magnitude and CoP position on motorcycle stability in straight-running conditions. To this end, we develop a motorcycle stability model and perform an analysis on a motorcycle with several CoP and downforce values. We consider the CoP ahead, aligned, and behind the motorcycle centre of mass, together with multiple lift coefficients. Results showed that CoP towards the front end stabilises wobble mode, while rear CoP may cause instability on weave mode. The result contributes to the understanding of motorcycle aerodynamics providing new insights into how to use aerodynamics to enhance stability.

The development of computationally efficient and validated single-track vehicle-rider models has traditionally required handcrafted one-off models. Here we introduce BRiM, a software package that facilitates building these models in a modular fashion while retaining access to the mathematical elements for handcrafted modeling when desired. We demonstrate the flexibility of the software by constructing the Carvallo-Whipple bicycle model with different numerical parameters representing different bicycles, modifying it with a front fork suspension travel model, and extending it with moving rider arms driven by joint torques at the elbows. Using these models we solve a lane-change optimal control problem for six different model variations which solve in mere seconds on a modern laptop. Our tool enables flexible and rapid modeling of single-track vehicle-rider models that give precise results at high computational efficiency.

This work presents the development of a Hardware-in-the-Loop (HIL) test bench that can be used to validate an electric bicycle (e-bike) anti-lock braking system (ABS) for different test scenarios. The approach involves interfacing a virtual bicycle simulation model running on a real-time target machine with the physical ABS hardware under test. This setup allows to test and evaluate ABS behavior in a safe and reproducible way, before starting testing on the track. This article describes the derivation of an equation-based model considering six degree-of-freedom (dof) representing the in-plane longitudinal dynamics of an e-bike. The simulation model is experimentally validated against measurements made on an instrumented test bike. The test apparatus used and the comparison of simulation results with measurements are presented. The characteristics of the HIL test bench developed are presented, and its applicability to an ABS validation process is illustrated by evaluating the braking performance of an ABS tested on a crossover bike.

Cyclists are usually afraid of using the front brake of their bicycles aggressively. They fear the danger of falling over the handlebar, sustaining serious neck or head injuries. Preventing this pitch-over can be addressed using electronic brake assistance. But little work is found on the dynamics involved, especially of the early phase were mitigating the pitch-over is still possible by brake pressure reduction. To address this, an instrumented bicycle equipped with sensors measuring variables of motion including absolute over ground velocity and attitude is presented. The need for a novel instrumented bicycle capable of capturing pitch-over dynamics and detecting when ground contact is lost, is pointed out. Needed sensors and their calibration is worked out, and the instrumented bicycle is built and tested. The capturing capabilities are shown, and robust jet precise methods of ground contact loss detection are presented.